Finite Group Databasebeta

← C2×#23777702 #35195396

Subgroups — C2×#23777702 #35195396

Order 20224.

8122 conjugacy classes of subgroups.

The subgroup lattice has 1444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777702C2132yesmaximal, direct product factor
2C2×#19099310C212yesmaximal, complemented
3C2×#19099301C212yesmaximal, complemented
4C2×#19099278C211yesmaximal, characteristic, complemented
5C2×#19099265C211yesmaximal, characteristic, complemented
6C2×#19099255C211yesmaximal, characteristic, complemented
7C2×#19099239C212yesmaximal, complemented
8C2×#19099232C211yesmaximal, characteristic, complemented
9C2×#19099217C211yesmaximal, characteristic, complemented
10C2×#19099206C211yesmaximal, characteristic, complemented
11C2×#19099200C212yesmaximal, complemented
12C2×D4×C22⋊D79C211yesmaximal, characteristic, complemented
13C2×#19099182C211yesmaximal, characteristic, complemented
14C2×#19099166C212yesmaximal, complemented
15C2×#19099164C211yesmaximal, characteristic, complemented
16C2×#19099149C212yesmaximal, complemented
17C2×#19099141C211yesmaximal, characteristic, complemented
18C2×#19099129C211yesmaximal, characteristic, complemented
19C2×#19099128C212yesmaximal, complemented
20C2×#19099125C212yesmaximal, complemented
21C2×#19099076C211yesmaximal, characteristic, complemented
22C2×#19099072C211yesmaximal, characteristic, complemented
23C22×#14579132C211yesmaximal, characteristic, complemented
24C2×#546×C79C211yesmaximal, characteristic, complemented
25C22×#11929625C2211yescharacteristic, complemented
26C22×#11929624C2211yescharacteristic, complemented
27C22×#11929623C2212yescomplemented
28C23×C22⋊D79C2212yes—
29C23×C22⋊D79C2212yescomplemented
30C22×D4×D79C2211yescharacteristic, complemented
31C23×C4×D79C2211yescharacteristic, complemented
32#19099310C22132yescomplemented
33#19099301C22132yescomplemented
34#19099278C22116yescomplemented
35#19099265C22116yescomplemented
36#19099255C22116yescomplemented
37#19099239C22132yescomplemented
38#19099232C22116yescomplemented
39#19099217C22116yescomplemented
40#19099206C22116yescomplemented
41#19099200C22132yescomplemented
42D4×C22⋊D79C22116yescomplemented
43#19099182C22116yescomplemented
44#19099166C22132yescomplemented
45#19099164C22116yescomplemented
46#19099149C22132yescomplemented
47#19099141C22116yescomplemented
48#19099129C22116yescomplemented
49#19099128C22132yescomplemented
50#19099125C22132yescomplemented
51C2×#14579161C2211yescharacteristic, complemented
52C2×#14579157C2211yescharacteristic, complemented
53C2×#14579157C2212yescomplemented
54C2×#14579157C2212yescomplemented
55C2×#14579156C2212yescomplemented
56C2×#14579154C2212yescomplemented
57C2×#14579154C2212yescomplemented
58C2×#14579152C2211yescharacteristic, complemented
59C2×#14579152C2212yescomplemented
60C2×#14579147C2212yescomplemented
61C2×#14579147C2212yescomplemented
62C2×#14579147C2212yescomplemented
63C2×#14579147C2212yescomplemented
64#19099076C22116yescomplemented
65#19099072C22116yescomplemented
66C2×#14579146C2211yescharacteristic, complemented
67C2×#14579146C2212yescomplemented
68C2×#14579145C2212yes—
69C2×#14579145C2212yescomplemented
70C2×#14579145C2212yescomplemented
71C2×#14579145C2212yescomplemented
72C2×#14579145C2212yescomplemented
73C2×#14579144C2212yescomplemented
74C2×#14579143C2212yescomplemented
75C2×#14579143C2212yescomplemented
76C2×#14579143C2211yescharacteristic, complemented
77C2×#14579141C2212yescomplemented
78C2×#14579140C2212yescomplemented
79C2×#14579139C2211yescharacteristic, complemented
80C2×#14579138C2212yescomplemented
81C2×#14579138C2211yescharacteristic, complemented
82C2×#14579137C2211yescharacteristic, complemented
83C2×#14579137C2211yescharacteristic, complemented
84C2×#14579136C2211yescharacteristic, complemented
85C2×#14579135C2211yescharacteristic
86C2×#14579135C2211yescharacteristic, complemented
87C2×#14579135C2212yescomplemented
88C2×#14579135C2212yescomplemented
89C2×#14579135C2212yescomplemented
90C2×#14579135C2212yescomplemented
91C2×#14579134C2212yescomplemented
92C2×#14579134C2211yescharacteristic, complemented
93C2×#14579134C2212yescomplemented
94C2×#14579133C2211yescharacteristic
95C2×#14579133C2212yescomplemented
96C2×#14579133C2212yescomplemented
97C2×#14579133C2212yescomplemented
98C2×#14579133C2212yescomplemented
99C2×#14579132C2211yescharacteristic
100C2×#14579132C2211yescharacteristic
101C2×#14579132C2211yescharacteristic, complemented
102C2×#14579132C2212yescomplemented
103C2×#14579132C2211yescharacteristic, complemented
104C2×#14579132C2211yescharacteristic, complemented
105C2×#14579132C2212yescomplemented
106C2×#14579132C2212yescomplemented
107C2×#14579132C22116yescomplemented
108C2×#14579131C2211yescharacteristic
109C2×#14579131C2212yescomplemented
110C2×#14579131C2212yescomplemented
111C2×#14579131C2212yescomplemented
112C2×#14579130C2212yes—
113C2×#14579129C2212yescomplemented
114C2×#14579129C2212yescomplemented
115C2×#14579129C2211yescharacteristic, complemented
116C2×Q8×Dic79C2211yescharacteristic, complemented
117C2×C4×D316C2211yescharacteristic, complemented
118C2×C4×D316C2211yescharacteristic, complemented
119C2×D4×Dic79C2211yescharacteristic, complemented
120C2×D4×Dic79C2212yescomplemented
121C2×#14579123C2212yescomplemented
122C2×C4×C22⋊D79C2211yescharacteristic
123C2×C4×C22⋊D79C2211yescharacteristic, complemented
124C2×C4×C22⋊D79C2212yescomplemented
125C2×(C22⋊D79)⋊C4C2212yescomplemented
126C2×#14579120C2212yescomplemented
127C2×#14579119C2211yescharacteristic, complemented
128C2×#14579119C2211yescharacteristic, complemented
129C2×#14579118C2211yescharacteristic, complemented
130C2×#14579117C2212yescomplemented
131C22×C4⋊Dic79C2211yescharacteristic, complemented
132C22×C4⋊Dic79C2211yescharacteristic, complemented
133C22×C22⋊Dic79C2212yescomplemented
134C2×C22⋊C4×D79C2212yescomplemented
135C22×#41×C79C2211yescharacteristic, complemented
136C23×D4×C79C2211yescharacteristic
137#546×C79C22116yescomplemented
138C2×#124×C79C2211yescharacteristic, complemented
139C2×#123×C79C2212yescomplemented
140C2×C22⋊Q8×C79C2211yescharacteristic, complemented
141C2×#121×C79C2211yescharacteristic, complemented
142C2×#121×C79C2212yescomplemented
143C2×#120×C79C2212yescomplemented
144C2×C4×D4×C79C2211yescharacteristic, complemented
145C2×C4×D4×C79C2211yescharacteristic, complemented
146C22×C22⋊C4×C79C2212yescomplemented
147C24×D79C2311yescharacteristic
148C24×D79C2312yes—
149C2×#11929625—44no—
150C2×#11929625C2318yescomplemented
151C2×#11929624—44no—
152C2×#11929624C2318yescomplemented
153C2×#11929623—48no—
154C2×#11929623C23116yescomplemented
155C22×Dic158C2311yescharacteristic
156C22×Dic158C2312yes—
157C22×D316C2311yescharacteristic
158C22×D316C2312yes—
159C22×D316C2311yescharacteristic
160C22×D316C2311yescharacteristic
161C22×D316C2312yes—
162C22×C22⋊D79—48no—
163C22×C22⋊D79—48no—
164C22×C22⋊D79C2312yes—
165C22×C22⋊D79C2311yescharacteristic
166C22×C22⋊D79C23116yes—
167C22×C22⋊D79C2312yes—
168C22×C22⋊D79C2311yescharacteristic
169C22×C22⋊D79C2311yescharacteristic
170C22×C22⋊D79C2312yes—
171C22×C22⋊D79C2312yes—
172C22×C22⋊D79C2311yescharacteristic
173C22×C22⋊D79C2312yes—
174C22×C22⋊D79C2312yes—
175C22×C22⋊D79C2312yes—
176C22×C22⋊D79C2312yes—
177C22×C22⋊D79C2312yes—
178C22×C22⋊D79C2312yes—
179C22×C22⋊D79C23116yescomplemented
180C2×D4×D79—44no—
181C2×D4×D79C2318yescomplemented
182C23×Dic79C2312yes—
183C23×Dic79C2311yescharacteristic
184C23×Dic79C2312yes—
185C23×Dic79C2312yes—
186C22×C4×D79—44no—
187C22×C4×D79C2311yescharacteristic
188C22×C4×D79C2311yescharacteristic
189C22×C4×D79C2311yescharacteristic
190C22×C4×D79C2312yes—
191C22×C4×D79C2312yes—
192C22×C4×D79C2311yescharacteristic
193C22×C4×D79C2311yescharacteristic
194C22×C4×D79C2318yescomplemented
195#14579161C2318yescomplemented
196#14579157C2318yescomplemented
197#14579157C23116yescomplemented
198#14579157C23116yescomplemented
199#14579156C23116yescomplemented
200#14579154C23116yescomplemented
201#14579154C23116yescomplemented
202#14579152C2318yescomplemented
203#14579152C23116yescomplemented
204#14579147C23116yescomplemented
205#14579147C23116yescomplemented
206#14579147C23116yescomplemented
207#14579147C23116yescomplemented
208#14579146C2318yescomplemented
209#14579146C23116yescomplemented
210#14579145C23116yes—
211#14579145C23116yescomplemented
212#14579145C23116yescomplemented
213#14579145C23116yescomplemented
214#14579145C23116yescomplemented
215#14579144C23116yescomplemented
216#14579143C23116yescomplemented
217#14579143C2318yescomplemented
218#14579143C23116yescomplemented
219#14579141C23116yescomplemented
220#14579140C23116yescomplemented
221#14579139C2318yescomplemented
222#14579138C23116yescomplemented
223#14579138C2318yescomplemented
224#14579137C2318yescomplemented
225#14579137C2318yescomplemented
226#14579136C2318yescomplemented
227#14579135C2318yes—
228#14579135C23116yescomplemented
229#14579135C23116yescomplemented
230#14579135C2318yescomplemented
231#14579135C23116yescomplemented
232#14579135C23116yescomplemented
233#14579134C23116yescomplemented
234#14579134C23116yescomplemented
235#14579134C2318yescomplemented
236#14579133C2318yes—
237#14579133C23116yescomplemented
238#14579133C23116yescomplemented
239#14579133C23116yescomplemented
240#14579133C23116yescomplemented
241#14579132C2318yes—
242#14579132C2318yes—
243#14579132C2318yescomplemented
244#14579132C2318yescomplemented
245#14579132C23116yescomplemented
246#14579132C23116yescomplemented
247#14579132C2318yescomplemented
248#14579132C23116yescomplemented
249#14579131C2318yes—
250#14579131C23116yescomplemented
251#14579131C23116yescomplemented
252#14579131C23116yescomplemented
253#14579130C23116yes—
254#14579129C23116yescomplemented
255#14579129C23116yescomplemented
256#14579129C2318yescomplemented
257Q8×Dic79C2318yescomplemented
258C4×D316C2318yescomplemented
259C4×D316C2318yescomplemented
260D4×Dic79C23116yescomplemented
261D4×Dic79C2318yescomplemented
262#14579123C23116yescomplemented
263C4×C22⋊D79C2318yes—
264C4×C22⋊D79C23116yescomplemented
265C4×C22⋊D79C2318yescomplemented
266(C22⋊D79)⋊C4C23116yescomplemented
267#14579120C23116yescomplemented
268#14579119C2318yescomplemented
269#14579119C2318yescomplemented
270#14579118C2318yescomplemented
271#14579117C23116yescomplemented
272C2×C4⋊Dic79C2311yescharacteristic
273C2×C4⋊Dic79C2311yescharacteristic
274C2×C4⋊Dic79C2311yescharacteristic
275C2×C4⋊Dic79C2312yes—
276C2×C4⋊Dic79C2312yes—
277C2×C4⋊Dic79C2311yescharacteristic
278C2×C4⋊Dic79C2312yes—
279C2×C4⋊Dic79C2312yes—
280C2×C4⋊Dic79C2312yes—
281C2×C4⋊Dic79C2318yescomplemented
282C2×C4⋊Dic79C2318yescomplemented
283C2×Dic79⋊C4C2312yes—
284C2×Dic79⋊C4C2312yes—
285C2×Dic79⋊C4C2311yescharacteristic
286C2×Dic79⋊C4C2311yescharacteristic
287C2×Dic79⋊C4C2312yes—
288C2×Dic79⋊C4C2311yescharacteristic
289C2×Dic79⋊C4C2311yescharacteristic
290C2×C22⋊Dic79C2312yes—
291C2×C22⋊Dic79C2312yes—
292C2×C22⋊Dic79C2312yes—
293C2×C22⋊Dic79C2312yes—
294C2×C22⋊Dic79C2311yescharacteristic
295C2×C22⋊Dic79C2312yes—
296C2×C22⋊Dic79C2311yescharacteristic
297C2×C22⋊Dic79C2312yes—
298C2×C22⋊Dic79C23116yescomplemented
299C2×(C2×D79)⋊C4C2311yescharacteristic
300C2×(C2×D79)⋊C4C2312yes—
301C2×(C2×D79)⋊C4C2311yescharacteristic
302C2×(C2×D79)⋊C4C2311yescharacteristic
303C2×(C2×D79)⋊C4C2312yes—
304C2×(C2×D79)⋊C4C2312yes—
305C2×(C2×D79)⋊C4C2312yes—
306C2×(C2×D79)⋊C4C2311yescharacteristic
307C2×(C2×D79)⋊C4C2311yescharacteristic
308C2×(C2×D79)⋊C4C2312yes—
309C2×(C2×D79)⋊C4C2312yes—
310C2×(C2×D79)⋊C4C2312yes—
311C2×(C2×D79)⋊C4C2311yescharacteristic
312C2×(C2×D79)⋊C4C2312yes—
313C22⋊C4×D79C23116yescomplemented
314C2×C4×Dic79C2312yes—
315C2×C4×Dic79C2312yes—
316C2×C4×Dic79C2311yescharacteristic
317C2×C4×Dic79C2312yes—
318C25×C79C2312yes—
319C2×#41×C79—44no—
320C2×#41×C79C2318yescomplemented
321C22×Q8×C79C2311yescharacteristic
322C22×D4×C79—44no—
323C22×D4×C79C2311yescharacteristic
324C22×D4×C79C2311yescharacteristic
325C22×D4×C79C2311yescharacteristic
326C22×D4×C79C2318yes—
327C22×D4×C79C2312yes—
328C22×D4×C79C2312yes—
329C22×D4×C79C2312yes—
330C23×C4×C79C2311yescharacteristic
331C23×C4×C79C2311yescharacteristic
332C23×C4×C79C2312yes—
333C23×C4×C79C2312yes—
334#124×C79C2318yescomplemented
335#123×C79C23116yescomplemented
336C22⋊Q8×C79C2318yescomplemented
337#121×C79C23116yescomplemented
338#121×C79C2318yescomplemented
339#120×C79C23116yescomplemented
340C4×D4×C79C2318yescomplemented
341C4×D4×C79C2318yescomplemented
342C2×C4⋊C4×C79C2311yescharacteristic
343C2×C4⋊C4×C79C2311yescharacteristic
344C2×C4⋊C4×C79C2312yes—
345C2×C22⋊C4×C79C2311yescharacteristic
346C2×C22⋊C4×C79C2312yes—
347C2×C22⋊C4×C79C2312yes—
348C2×C22⋊C4×C79C2312yes—
349C2×C22⋊C4×C79C2312yes—
350C2×C22⋊C4×C79C2311yescharacteristic
351C2×C22⋊C4×C79C2312yes—
352C2×C22⋊C4×C79C23116yescomplemented
353C2×C42×C79C2311yescharacteristic
354C23×D79—24no—
355C23×D79—42no—
356C23×D79—42no—
357C23×D79—44no—
358C23×D79—44no—
359C23×D79—44no—
360C23×D79C2411yescharacteristic
361C23×D79C2411yescharacteristic
362C23×D79C2411yescharacteristic
363C23×D79C2412yes—
364C23×D79C2414yes—
365C23×D79C2418yes—
366#11929625—416no—
367#11929624—416no—
368#11929623—432no—
369C2×Dic158—44no—
370C2×Dic158—42no—
371C2×Dic158C2418yes—
372C2×Dic158C2414yes—
373C2×D316—24no—
374C2×D316—42no—
375C2×D316—44no—
376C2×D316—42no—
377C2×D316—44no—
378C2×D316C2414yes—
379C2×D316C2414yes—
380C2×D316C2418yes—
381C2×D316C2418yes—
382C2×D316C2414yes—
383C2×C22⋊D79—28no—
384C2×C22⋊D79—24no—
385C2×C22⋊D79—432no—
386C2×C22⋊D79—44no—
387C2×C22⋊D79—42no—
388C2×C22⋊D79—42no—
389C2×C22⋊D79—44no—
390C2×C22⋊D79—44no—
391C2×C22⋊D79—44no—
392C2×C22⋊D79—44no—
393C2×C22⋊D79—44no—
394C2×C22⋊D79—44no—
395C2×C22⋊D79—44no—
396C2×C22⋊D79—432no—
397C2×C22⋊D79—44no—
398C2×C22⋊D79—42no—
399C2×C22⋊D79C2418yes—
400C2×C22⋊D79C2414yes—
401C2×C22⋊D79C2418yes—
402C2×C22⋊D79C2414yes—
403C2×C22⋊D79C2414yes—
404C2×C22⋊D79C2418yes—
405C2×C22⋊D79C2414yes—
406C2×C22⋊D79C2418yes—
407C2×C22⋊D79C2418yes—
408C2×C22⋊D79C2418yes—
409C2×C22⋊D79C2418yes—
410C2×C22⋊D79C2418yes—
411C2×C22⋊D79C2418yes—
412C2×C22⋊D79C2418yes—
413D4×D79—416no—
414C22×Dic79—28no—
415C22×Dic79—44no—
416C22×Dic79—42no—
417C22×Dic79—44no—
418C22×Dic79C2412yes—
419C22×Dic79C2411yescharacteristic
420C22×Dic79C2412yes—
421C22×Dic79C2411yescharacteristic
422C22×Dic79C2418yes—
423C22×Dic79C2411yescharacteristic
424C22×Dic79C2411yescharacteristic
425C22×Dic79C2411yescharacteristic
426C22×Dic79C2412yes—
427C22×Dic79C2418yes—
428C22×Dic79C2414yes—
429C22×Dic79C2418yes—
430C2×C4×D79—24no—
431C2×C4×D79—24no—
432C2×C4×D79—24no—
433C2×C4×D79—44no—
434C2×C4×D79—44no—
435C2×C4×D79—42no—
436C2×C4×D79—42no—
437C2×C4×D79—416no—
438C2×C4×D79C2414yes—
439C2×C4×D79C2414yes—
440C2×C4×D79C2414yes—
441C2×C4×D79C2418yes—
442C2×C4×D79C2418yes—
443C2×C4×D79C2414yes—
444C2×C4×D79C2414yes—
445C4⋊Dic79C2414yes—
446C4⋊Dic79C2414yes—
447C4⋊Dic79C2414yes—
448C4⋊Dic79C2418yes—
449C4⋊Dic79C2418yes—
450C4⋊Dic79C2414yes—
451C4⋊Dic79C2418yes—
452C4⋊Dic79C2418yes—
453C4⋊Dic79C2418yes—
454Dic79⋊C4C2418yes—
455Dic79⋊C4C2418yes—
456Dic79⋊C4C2414yes—
457Dic79⋊C4C2414yes—
458Dic79⋊C4C2418yes—
459Dic79⋊C4C2414yes—
460Dic79⋊C4C2414yes—
461C22⋊Dic79C2418yes—
462C22⋊Dic79C2418yes—
463C22⋊Dic79C2418yes—
464C22⋊Dic79C2418yes—
465C22⋊Dic79C2414yes—
466C22⋊Dic79C2418yes—
467C22⋊Dic79C2414yes—
468C22⋊Dic79C2418yes—
469(C2×D79)⋊C4C2414yes—
470(C2×D79)⋊C4C2418yes—
471(C2×D79)⋊C4C2414yes—
472(C2×D79)⋊C4C2414yes—
473(C2×D79)⋊C4C2418yes—
474(C2×D79)⋊C4C2418yes—
475(C2×D79)⋊C4C2418yes—
476(C2×D79)⋊C4C2414yes—
477(C2×D79)⋊C4C2414yes—
478(C2×D79)⋊C4C2418yes—
479(C2×D79)⋊C4C2418yes—
480(C2×D79)⋊C4C2418yes—
481(C2×D79)⋊C4C2414yes—
482(C2×D79)⋊C4C2418yes—
483C4×Dic79C2418yes—
484C4×Dic79C2418yes—
485C4×Dic79C2414yes—
486C4×Dic79C2418yes—
487C24×C79—28no—
488C24×C79—44no—
489C24×C79—44no—
490C24×C79C2412yes—
491C24×C79C2412yes—
492C24×C79C2411yescharacteristic
493C24×C79C2411yescharacteristic
494C24×C79C2418yes—
495#41×C79—416no—
496C2×Q8×C79—24no—
497C2×Q8×C79C2414yes—
498C2×D4×C79—24no—
499C2×D4×C79—24no—
500C2×D4×C79—24no—
501C2×D4×C79—416no—
502C2×D4×C79—44no—
503C2×D4×C79—44no—
504C2×D4×C79—44no—
505C2×D4×C79C2414yes—
506C2×D4×C79C2414yes—
507C2×D4×C79C2414yes—
508C2×D4×C79C2418yes—
509C2×D4×C79C2418yes—
510C2×D4×C79C2418yes—
511C22×C4×C79—24no—
512C22×C4×C79—24no—
513C22×C4×C79—44no—
514C22×C4×C79—44no—
515C22×C4×C79C2411yescharacteristic
516C22×C4×C79C2411yescharacteristic
517C22×C4×C79C2414yes—
518C22×C4×C79C2411yescharacteristic
519C22×C4×C79C2412yes—
520C22×C4×C79C2412yes—
521C22×C4×C79C2411yescharacteristic
522C22×C4×C79C2414yes—
523C22×C4×C79C2418yes—
524C22×C4×C79C2418yes—
525C22×C4×C79C2411yescharacteristic
526C4⋊C4×C79C2414yes—
527C4⋊C4×C79C2414yes—
528C4⋊C4×C79C2418yes—
529C22⋊C4×C79C2414yes—
530C22⋊C4×C79C2418yes—
531C22⋊C4×C79C2418yes—
532C22⋊C4×C79C2418yes—
533C22⋊C4×C79C2418yes—
534C22⋊C4×C79C2414yes—
535C22⋊C4×C79C2418yes—
536C42×C79C2414yes—
537C23×C79—22no—
538C23×C79—22no—
539C23×C79—22no—
540C23×C79—24no—
541C23×C79—24no—
542C23×C79—22no—
543C23×C79—24no—
544C23×C79—24no—
545C23×C79—24no—
546C23×C79—22no—
547C23×C79—24no—
548C23×C79—216no—
549C23×C79—48no—
550C23×C79—48no—
551C23×C79—816no—
552C23×C79H(5,𝔽2)14yes—
553C23×C79C2514yes—
554C23×C79C2514yes—
555C23×C79C2512yes—
556C23×C79C2512yes—
557C23×C79C2511yescharacteristic
558C22×D79—22no—
559C22×D79—22no—
560C22×D79—22no—
561C22×D79—24no—
562C22×D79—24no—
563C22×D79—22no—
564C22×D79—28no—
565C22×D79—22no—
566C22×D79—22no—
567C22×D79—22no—
568C22×D79—24no—
569C22×D79—22no—
570C22×D79—22no—
571C22×D79—44no—
572C22×D79—44no—
573C22×D79—48no—
574C22×D79—48no—
575C22×D79—48no—
576C22×D79—416no—
577C22×D79—816no—
578C22×D79C2512yes—
579C22×D79C2514yes—
580C22×D79C2512yes—
581C22×D79C2512yes—
582Q8×C79—28no—
583D4×C79—28no—
584D4×C79—28no—
585D4×C79—28no—
586D4×C79—48no—
587D4×C79—48no—
588D4×C79—48no—
589C2×C4×C79—22no—
590C2×C4×C79—22no—
591C2×C4×C79—24no—
592C2×C4×C79—22no—
593C2×C4×C79—22no—
594C2×C4×C79—24no—
595C2×C4×C79—28no—
596C2×C4×C79—28no—
597C2×C4×C79—48no—
598C2×C4×C79—48no—
599C2×C4×C79H(5,𝔽2)14yes—
600C2×C4×C79C2514yes—
601C2×C4×C79C2514yes—
602C2×C4×C79C2512yes—
603C2×C4×C79C2512yes—
604C2×C4×C79C2512yes—
605C2×C4×C79C2512yes—
606C2×C4×C79C2512yes—
607C22⋊D79—28no—
608C22⋊D79—216no—
609C22⋊D79—48no—
610C22⋊D79—48no—
611C22⋊D79—48no—
612C22⋊D79—48no—
613C22⋊D79—48no—
614C22⋊D79—48no—
615C22⋊D79—48no—
616C22⋊D79—48no—
617C22⋊D79—44no—
618C22⋊D79—48no—
619C22⋊D79—44no—
620C22⋊D79—44no—
621C2×Dic79—22no—
622C2×Dic79—22no—
623C2×Dic79—22no—
624C2×Dic79—24no—
625C2×Dic79—24no—
626C2×Dic79—216no—
627C2×Dic79—22no—
628C2×Dic79—24no—
629C2×Dic79—22no—
630C2×Dic79—44no—
631C2×Dic79—48no—
632C2×Dic79—48no—
633C2×Dic79C2512yes—
634C2×Dic79C2514yes—
635C2×Dic79C2512yes—
636C2×Dic79C2512yes—
637C2×Dic79C2514yes—
638C2×Dic79C2512yes—
639C2×Dic79C2512yes—
640C2×Dic79C2514yes—
641D316—28no—
642D316—44no—
643D316—48no—
644D316—44no—
645D316—48no—
646C4×D79—28no—
647C4×D79—28no—
648C4×D79—28no—
649C4×D79—44no—
650C4×D79—44no—
651C4×D79—48no—
652C4×D79—48no—
653Dic158—48no—
654Dic158—44no—
655C22×C79—22no—
656C22×C79—22no—
657C22×C79—28no—
658C22×C79—24no—
659C22×C79—22no—
660C22×C79—22no—
661C22×C79—24no—
662C22×C79—24no—
663C22×C79—24no—
664C22×C79—24no—
665C22×C79—22no—
666C22×C79—24no—
667C22×C79—48no—
668C22×C79—44no—
669C22×C79—48no—
670C22×C79—816no—
671C22×C79C2×H(5,𝔽2)12yes—
672C22×C79C2×H(5,𝔽2)14yes—
673C22×C79C2×H(5,𝔽2)12yes—
674C22×C79#58512yes—
675C22×C79C2611yescharacteristic
676C2×D79—22no—
677C2×D79—24no—
678C2×D79—22no—
679C2×D79—22no—
680C2×D79—22no—
681C2×D79—22no—
682C2×D79—24no—
683C2×D79—22no—
684C2×D79—22no—
685C2×D79—24no—
686C2×D79—22no—
687C2×D79—22no—
688C2×D79—416no—
689C2×D79—44no—
690C2×D79—44no—
691C2×D79—48no—
692C2×D79—44no—
693C2×D79—816no—
694C4×C79—22no—
695C4×C79—22no—
696C4×C79—24no—
697C4×C79—22no—
698C4×C79—22no—
699C4×C79—24no—
700C4×C79C2×H(5,𝔽2)14yes—
701Dic79—22no—
702Dic79—24no—
703Dic79—22no—
704Dic79—24no—
705Dic79—24no—
706Dic79—22no—
707Dic79—22no—
708Dic79—22no—
709C2×#3542—791nomaximal, Sylow
710C2×C79—24no—
711C2×C79—44no—
712C2×C79—42no—
713C2×C79—44no—
714C2×C79#354214yescomplemented
715C2×C79C22×H(5,𝔽2)11yescharacteristic
716C2×C79C22×H(5,𝔽2)11yescharacteristic
717C2×C79C2×#58511yescharacteristic
718D79—42no—
719D79—42no—
720D79—44no—
721D79—42no—
722#3542—7932no—
723C2×#562—792no—
724C2×#560—792no—
725C2×#555—791no—
726C2×#553—791no—
727C2×#552—791no—
728C2×#551—792no—
729C2×#550—791no—
730C2×#547—791no—
731C2×#546—791no—
732C2×#546—792no—
733C2×#546D7911yescharacteristic, complemented
734C2×D42—791no—
735C2×#542—791no—
736C2×#540—792no—
737C2×#540—791no—
738C2×#538—792no—
739C2×#537—791no—
740C2×#535—791no—
741C2×#535—792no—
742C2×#534—792no—
743C2×#525—791no—
744C2×#525—791no—
745C22×#121—791no—
746C79C2×#354211yescharacteristic, complemented, Sylow
747C22×#41—791no—
748C22×#41—792no—
749C22×#41—791no—
750C22×#41C2×D7911yescharacteristic, complemented
751C23×D4—792no—
752C23×D4—792no—
753C23×D4—791no—
754C23×D4C2×D7911yescharacteristic
755C24×C4—791no—
756#562—7932no—
757#560—7932no—
758#555—7916no—
759#553—7916no—
760#552—7916no—
761#551—7932no—
762#550—7916no—
763#547—7916no—
764#546—7916no—
765#546—7932no—
766#546C2×D79116yescomplemented
767D42—7916no—
768#542—7916no—
769#540—7932no—
770#540—7916no—
771#538—7932no—
772#537—7916no—
773#535—7916no—
774#535—7932no—
775#534—7932no—
776C2×C4⋊Q8—791no—
777C2×#127—792no—
778C2×#127—792no—
779C2×#127—791no—
780C2×#126—792no—
781C2×#126—792no—
782C2×#126—792no—
783C2×#125—791no—
784C2×#125—792no—
785C2×#124—792no—
786C2×#124—792no—
787C2×#124—792no—
788C2×#124—792no—
789C2×#124C2×D7911yescharacteristic, complemented
790#525—7916no—
791#525—7916no—
792C2×#123—792no—
793C2×#123—791no—
794C2×#123—792no—
795C2×#123—791no—
796C2×#123—792no—
797C2×#123—792no—
798C2×#123—792no—
799C2×#123—792no—
800C2×#123—792no—
801C2×#123—792no—
802C2×#123—792no—
803C2×#123C2×D7912yescomplemented
804C2×C22⋊Q8—791no—
805C2×C22⋊Q8—791no—
806C2×C22⋊Q8—792no—
807C2×C22⋊Q8—791no—
808C2×C22⋊Q8—792no—
809C2×C22⋊Q8—791no—
810C2×C22⋊Q8—792no—
811C2×C22⋊Q8C2×D7911yescharacteristic, complemented
812C2×#121—791no—
813C2×#121—791no—
814C2×#121—792no—
815C2×#121—791no—
816C2×#121—791no—
817C2×#121—792no—
818C2×#121—7916no—
819C2×#121—791no—
820C2×#121—792no—
821C2×#121—792no—
822C2×#121—791no—
823C2×#121—792no—
824C2×#121—792no—
825C2×#121—792no—
826C2×#121—791no—
827C2×#121—792no—
828C2×#121—792no—
829C2×#121—792no—
830C2×#121—792no—
831C2×#121—791no—
832C2×#121—791no—
833C2×#121—791no—
834C2×#121—792no—
835C2×#121—792no—
836C2×#121C2×D7911yescharacteristic, complemented
837C2×#121C2×D7912yescomplemented
838C2×#120—792no—
839C2×#120—791no—
840C2×#120—792no—
841C2×#120—792no—
842C2×#120—791no—
843C2×#120—792no—
844C2×#120—792no—
845C2×#120—792no—
846C2×#120C2×D7912yescomplemented
847C2×C4×Q8—791no—
848C2×C4×D4—792no—
849C2×C4×D4—791no—
850C2×C4×D4—791no—
851C2×C4×D4—791no—
852C2×C4×D4—792no—
853C2×C4×D4—792no—
854C2×C4×D4—792no—
855C2×C4×D4—791no—
856C2×C4×D4—791no—
857C2×C4×D4C2×D7911yescharacteristic, complemented
858C2×C4×D4C2×D7911yescharacteristic, complemented
859C2×#117—792no—
860C2×#117—791no—
861C2×#117—791no—
862C2×#117—792no—
863C2×#117—791no—
864C22×C4⋊C4—791no—
865C22×C4⋊C4—791no—
866C22×C22⋊C4—792no—
867C22×C22⋊C4—792no—
868C22×C22⋊C4C2×D7912yescomplemented
869C25—792no—
870C25—791no—
871C25C22×D7912yes—
872C2×#41—44no—
873C2×#41—3164no—
874C2×#41—3168no—
875C2×#41—3164no—
876C2×#41—798no—
877C2×#41—7916no—
878C2×#41—798no—
879C2×#41C22×D7918yescomplemented
880C22×Q8—791no—
881C22×Q8—792no—
882C22×Q8C22×D7911yescharacteristic
883C22×D4—44no—
884C22×D4—3168no—
885C22×D4—3164no—
886C22×D4—3168no—
887C22×D4—792no—
888C22×D4—791no—
889C22×D4—791no—
890C22×D4—792no—
891C22×D4—792no—
892C22×D4—792no—
893C22×D4—792no—
894C22×D4—791no—
895C22×D4—792no—
896C22×D4—792no—
897C22×D4—792no—
898C22×D4—792no—
899C22×D4—7916no—
900C22×D4—7916no—
901C22×D4—798no—
902C22×D4—792no—
903C22×D4—791no—
904C22×D4—791no—
905C22×D4—792no—
906C22×D4—791no—
907C22×D4—792no—
908C22×D4—791no—
909C22×D4C22×D7911yescharacteristic
910C22×D4C22×D7911yescharacteristic
911C22×D4C22×D7911yescharacteristic
912C22×D4C22×D7912yes—
913C22×D4C22×D7912yes—
914C22×D4C22×D7912yes—
915C22×D4C22×D7918yes—
916C23×C4—3164no—
917C23×C4—791no—
918C23×C4—792no—
919C23×C4—792no—
920C23×C4—792no—
921C23×C4—792no—
922C23×C4—791no—
923C23×C4—791no—
924C23×C4—798no—
925C23×C4—792no—
926C23×C4—791no—
927C23×C4—791no—
928C23×C4—791no—
929C23×C4C22×D7911yescharacteristic
930C23×C4C22×D7911yescharacteristic
931C23×C4C22×D7912yes—
932C23×C4C22×D7912yes—
933C4⋊Q8—798no—
934#127—7916no—
935#127—7916no—
936#127—798no—
937#126—7916no—
938#126—7916no—
939#126—7916no—
940#125—798no—
941#125—7916no—
942#124—7916no—
943#124—7916no—
944#124—7916no—
945#124—7916no—
946#124C22×D7918yescomplemented
947#123—7916no—
948#123—798no—
949#123—7916no—
950#123—798no—
951#123—7916no—
952#123—7916no—
953#123—7916no—
954#123—7916no—
955#123—7916no—
956#123—7916no—
957#123—7916no—
958#123C22×D79116yescomplemented
959C22⋊Q8—798no—
960C22⋊Q8—798no—
961C22⋊Q8—7916no—
962C22⋊Q8—798no—
963C22⋊Q8—7916no—
964C22⋊Q8—798no—
965C22⋊Q8—7916no—
966C22⋊Q8C22×D7918yescomplemented
967#121—798no—
968#121—798no—
969#121—7916no—
970#121—798no—
971#121—798no—
972#121—7916no—
973#121—798no—
974#121—7916no—
975#121—7916no—
976#121—798no—
977#121—7916no—
978#121—7916no—
979#121—7916no—
980#121—798no—
981#121—7916no—
982#121—7916no—
983#121—7916no—
984#121—7916no—
985#121—798no—
986#121—798no—
987#121—798no—
988#121—7916no—
989#121—7916no—
990#121C22×D7918yescomplemented
991#121C22×D79116yescomplemented
992#120—7916no—
993#120—798no—
994#120—7916no—
995#120—7916no—
996#120—798no—
997#120—7916no—
998#120—7916no—
999#120—7916no—
1000#120C22×D79116yescomplemented
1001C4×Q8—798no—
1002C4×D4—7916no—
1003C4×D4—798no—
1004C4×D4—798no—
1005C4×D4—798no—
1006C4×D4—7916no—
1007C4×D4—7916no—
1008C4×D4—7916no—
1009C4×D4—798no—
1010C4×D4—798no—
1011C4×D4C22×D7918yescomplemented
1012C4×D4C22×D7918yescomplemented
1013#117—7916no—
1014#117—798no—
1015#117—798no—
1016#117—7916no—
1017#117—798no—
1018C2×C4⋊C4—791no—
1019C2×C4⋊C4—791no—
1020C2×C4⋊C4—791no—
1021C2×C4⋊C4—792no—
1022C2×C4⋊C4—798no—
1023C2×C4⋊C4—792no—
1024C2×C4⋊C4—798no—
1025C2×C4⋊C4—791no—
1026C2×C4⋊C4—792no—
1027C2×C4⋊C4—792no—
1028C2×C4⋊C4—791no—
1029C2×C4⋊C4—791no—
1030C2×C4⋊C4—792no—
1031C2×C4⋊C4—791no—
1032C2×C4⋊C4—791no—
1033C2×C4⋊C4—792no—
1034C2×C4⋊C4—792no—
1035C2×C4⋊C4—792no—
1036C2×C4⋊C4C22×D7911yescharacteristic
1037C2×C4⋊C4C22×D7912yes—
1038C2×C4⋊C4C22×D7911yescharacteristic
1039C2×C22⋊C4—792no—
1040C2×C22⋊C4—792no—
1041C2×C22⋊C4—792no—
1042C2×C22⋊C4—792no—
1043C2×C22⋊C4—7916no—
1044C2×C22⋊C4—791no—
1045C2×C22⋊C4—792no—
1046C2×C22⋊C4—791no—
1047C2×C22⋊C4—792no—
1048C2×C22⋊C4—791no—
1049C2×C22⋊C4—792no—
1050C2×C22⋊C4—792no—
1051C2×C22⋊C4—791no—
1052C2×C22⋊C4—792no—
1053C2×C22⋊C4—791no—
1054C2×C22⋊C4—791no—
1055C2×C22⋊C4—792no—
1056C2×C22⋊C4—791no—
1057C2×C22⋊C4—792no—
1058C2×C22⋊C4—792no—
1059C2×C22⋊C4—791no—
1060C2×C22⋊C4—792no—
1061C2×C22⋊C4—792no—
1062C2×C22⋊C4—7916no—
1063C2×C22⋊C4C22×D7912yes—
1064C2×C22⋊C4C22×D7911yescharacteristic
1065C2×C22⋊C4C22×D7912yes—
1066C2×C22⋊C4C22×D7912yes—
1067C2×C22⋊C4C22×D7912yes—
1068C2×C22⋊C4C22×D7912yes—
1069C2×C22⋊C4C22×D7911yescharacteristic
1070C2×C22⋊C4C22×D79116yescomplemented
1071C2×C42—792no—
1072C2×C42—792no—
1073C2×C42—791no—
1074C2×C42—792no—
1075C2×C42C22×D7911yescharacteristic
1076C24—28no—
1077C24—44no—
1078C24—44no—
1079C24—3162no—
1080C24—3162no—
1081C24—3164no—
1082C24—3164no—
1083C24—3164no—
1084C24—798no—
1085C24—794no—
1086C24—791no—
1087C24—791no—
1088C24—791no—
1089C24—792no—
1090C24—1584no—
1091C24C23×D7912yes—
1092C24C23×D7912yes—
1093C24C23×D7911yescharacteristic
1094C24C23×D7911yescharacteristic
1095C24C23×D7918yes—
1096#41—416no—
1097#41—31616no—
1098#41—31632no—
1099#41—31616no—
1100C2×Q8—24no—
1101C2×Q8—3162no—
1102C2×Q8—3164no—
1103C2×Q8—794no—
1104C2×Q8—798no—
1105C2×Q8C23×D7914yes—
1106C2×D4—24no—
1107C2×D4—24no—
1108C2×D4—24no—
1109C2×D4—416no—
1110C2×D4—44no—
1111C2×D4—44no—
1112C2×D4—44no—
1113C2×D4—3162no—
1114C2×D4—3164no—
1115C2×D4—3162no—
1116C2×D4—3164no—
1117C2×D4—31632no—
1118C2×D4—31616no—
1119C2×D4—3164no—
1120C2×D4—3164no—
1121C2×D4—3164no—
1122C2×D4—3164no—
1123C2×D4—3164no—
1124C2×D4—3164no—
1125C2×D4—3164no—
1126C2×D4—31632no—
1127C2×D4—3164no—
1128C2×D4—3162no—
1129C2×D4—3162no—
1130C2×D4—3162no—
1131C2×D4—3164no—
1132C2×D4—798no—
1133C2×D4—794no—
1134C2×D4—794no—
1135C2×D4—798no—
1136C2×D4—798no—
1137C2×D4—798no—
1138C2×D4—798no—
1139C2×D4—798no—
1140C2×D4—794no—
1141C2×D4—798no—
1142C2×D4—798no—
1143C2×D4—798no—
1144C2×D4—798no—
1145C2×D4—794no—
1146C2×D4—794no—
1147C2×D4—798no—
1148C2×D4—794no—
1149C2×D4—798no—
1150C2×D4—794no—
1151C2×D4—1584no—
1152C2×D4—1588no—
1153C2×D4—1584no—
1154C2×D4C23×D7914yes—
1155C2×D4C23×D7914yes—
1156C2×D4C23×D7914yes—
1157C2×D4C23×D7918yes—
1158C2×D4C23×D7918yes—
1159C2×D4C23×D7918yes—
1160C22×C4—24no—
1161C22×C4—24no—
1162C22×C4—44no—
1163C22×C4—44no—
1164C22×C4—3162no—
1165C22×C4—3162no—
1166C22×C4—3164no—
1167C22×C4—3164no—
1168C22×C4—31616no—
1169C22×C4—3162no—
1170C22×C4—3164no—
1171C22×C4—3164no—
1172C22×C4—794no—
1173C22×C4—798no—
1174C22×C4—798no—
1175C22×C4—798no—
1176C22×C4—798no—
1177C22×C4—794no—
1178C22×C4—794no—
1179C22×C4—798no—
1180C22×C4—791no—
1181C22×C4—791no—
1182C22×C4—791no—
1183C22×C4—792no—
1184C22×C4—792no—
1185C22×C4—791no—
1186C22×C4—791no—
1187C22×C4—792no—
1188C22×C4—794no—
1189C22×C4—794no—
1190C22×C4—794no—
1191C22×C4—1588no—
1192C22×C4—1584no—
1193C22×C4—1584no—
1194C22×C4—1584no—
1195C22×C4C23×D7914yes—
1196C22×C4C23×D7914yes—
1197C22×C4C23×D7912yes—
1198C22×C4C23×D7912yes—
1199C22×C4C23×D7911yescharacteristic
1200C22×C4C23×D7911yescharacteristic
1201C22×C4C23×D7911yescharacteristic
1202C22×C4C23×D7911yescharacteristic
1203C22×C4C23×D7918yes—
1204C22×C4C23×D7918yes—
1205C22×C4C23×D7911yescharacteristic
1206C4⋊C4—798no—
1207C4⋊C4—798no—
1208C4⋊C4—794no—
1209C4⋊C4—794no—
1210C4⋊C4—794no—
1211C4⋊C4—794no—
1212C4⋊C4—798no—
1213C4⋊C4—794no—
1214C4⋊C4—794no—
1215C4⋊C4—794no—
1216C4⋊C4—798no—
1217C4⋊C4—798no—
1218C4⋊C4—794no—
1219C4⋊C4—798no—
1220C4⋊C4—798no—
1221C4⋊C4—798no—
1222C4⋊C4C23×D7914yes—
1223C4⋊C4C23×D7918yes—
1224C4⋊C4C23×D7914yes—
1225C22⋊C4—798no—
1226C22⋊C4—798no—
1227C22⋊C4—798no—
1228C22⋊C4—798no—
1229C22⋊C4—794no—
1230C22⋊C4—798no—
1231C22⋊C4—794no—
1232C22⋊C4—798no—
1233C22⋊C4—794no—
1234C22⋊C4—798no—
1235C22⋊C4—798no—
1236C22⋊C4—794no—
1237C22⋊C4—798no—
1238C22⋊C4—794no—
1239C22⋊C4—794no—
1240C22⋊C4—798no—
1241C22⋊C4—794no—
1242C22⋊C4—798no—
1243C22⋊C4—798no—
1244C22⋊C4—794no—
1245C22⋊C4—798no—
1246C22⋊C4—798no—
1247C22⋊C4C23×D7918yes—
1248C22⋊C4C23×D7914yes—
1249C22⋊C4C23×D7918yes—
1250C22⋊C4C23×D7918yes—
1251C22⋊C4C23×D7918yes—
1252C22⋊C4C23×D7918yes—
1253C22⋊C4C23×D7914yes—
1254C42—798no—
1255C42—798no—
1256C42—794no—
1257C42—798no—
1258C42C23×D7914yes—
1259C23—22no—
1260C23—22no—
1261C23—22no—
1262C23—24no—
1263C23—24no—
1264C23—22no—
1265C23—24no—
1266C23—24no—
1267C23—24no—
1268C23—22no—
1269C23—24no—
1270C23—216no—
1271C23—48no—
1272C23—48no—
1273C23—816no—
1274C23—31616no—
1275C23—3164no—
1276C23—3164no—
1277C23—3168no—
1278C23—3168no—
1279C23—3168no—
1280C23—792no—
1281C23—792no—
1282C23—792no—
1283C23—794no—
1284C23—63216no—
1285C23—1582no—
1286C23—1582no—
1287C23—1584no—
1288C23—1582no—
1289C23—1584no—
1290C23—1588no—
1291C23—1582no—
1292C23—1582no—
1293C23—1582no—
1294C23—1582no—
1295C23—1582no—
1296C23—1584no—
1297C23—1582no—
1298C23#1457920714yes—
1299C23C24×D7914yes—
1300C23C24×D7914yes—
1301C23C24×D7912yes—
1302C23C24×D7912yes—
1303C23C24×D7911yescharacteristic
1304Q8—28no—
1305Q8—3164no—
1306Q8—3168no—
1307D4—28no—
1308D4—28no—
1309D4—28no—
1310D4—48no—
1311D4—48no—
1312D4—48no—
1313D4—3164no—
1314D4—3168no—
1315D4—3164no—
1316D4—3168no—
1317D4—3168no—
1318D4—3168no—
1319D4—3168no—
1320D4—3168no—
1321D4—3168no—
1322D4—3168no—
1323D4—3168no—
1324D4—3168no—
1325D4—3164no—
1326D4—3164no—
1327D4—3164no—
1328D4—3168no—
1329D4—1588no—
1330D4—15816no—
1331D4—1588no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—24no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—24no—
1338C2×C4—28no—
1339C2×C4—28no—
1340C2×C4—48no—
1341C2×C4—48no—
1342C2×C4—3164no—
1343C2×C4—3164no—
1344C2×C4—3168no—
1345C2×C4—3168no—
1346C2×C4—3164no—
1347C2×C4—3168no—
1348C2×C4—3168no—
1349C2×C4—792no—
1350C2×C4—792no—
1351C2×C4—792no—
1352C2×C4—794no—
1353C2×C4—794no—
1354C2×C4—792no—
1355C2×C4—792no—
1356C2×C4—794no—
1357C2×C4—1582no—
1358C2×C4—1582no—
1359C2×C4—1582no—
1360C2×C4—1584no—
1361C2×C4—1582no—
1362C2×C4—1584no—
1363C2×C4—1584no—
1364C2×C4—15816no—
1365C2×C4—1582no—
1366C2×C4—1588no—
1367C2×C4—1588no—
1368C2×C4—1588no—
1369C2×C4#1457920614yes—
1370C2×C4C24×D7914yes—
1371C2×C4C24×D7914yes—
1372C2×C4C24×D7912yes—
1373C2×C4C24×D7912yes—
1374C2×C4C24×D7912yes—
1375C2×C4C24×D7912yes—
1376C2×C4C24×D7912yes—
1377C22—22no—
1378C22—22no—
1379C22—28no—
1380C22—22no—
1381C22—24no—
1382C22—24no—
1383C22—22no—
1384C22—24no—
1385C22—24no—
1386C22—24no—
1387C22—22no—
1388C22—24no—
1389C22—48no—
1390C22—48no—
1391C22—44no—
1392C22—816no—
1393C22—31616no—
1394C22—3164no—
1395C22—3164no—
1396C22—3164no—
1397C22—3168no—
1398C22—63216no—
1399C22—1582no—
1400C22—1582no—
1401C22—1584no—
1402C22—1582no—
1403C22—1584no—
1404C22—1582no—
1405C22—1582no—
1406C22—1582no—
1407C22—1582no—
1408C22—1582no—
1409C22—1584no—
1410C22—1582no—
1411C22C2×#1457920612yes—
1412C22C2×#1457920714yes—
1413C22C2×#1457920712yes—
1414C22#1909939812yes—
1415C22C25×D7911yescharacteristic
1416C4—22no—
1417C4—22no—
1418C4—24no—
1419C4—22no—
1420C4—22no—
1421C4—24no—
1422C4—1582no—
1423C4—1582no—
1424C4—1582no—
1425C4—1584no—
1426C4—1582no—
1427C4—1584no—
1428C4—1584no—
1429C4—1582no—
1430C4C2×#1457920614yes—
1431C2—24no—
1432C2—44no—
1433C2—44no—
1434C2—42no—
1435C2—3162no—
1436C2—3162no—
1437C2—3162no—
1438C2—3164no—
1439C2#2377770214yesdirect product factor
1440C2C22×#1457920611yescharacteristic
1441C2C22×#1457920711yescharacteristic
1442C2C2×#1909939811yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#546×C79C2
socleC23×C79C25
hypercenterC2×#546D79
hypocenterC79C2×#3542
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#546

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #23777702C2direct (N × H)
2. C2×#19099310C2semidirect
3. C2×#19099301C2semidirect
4. C2×#19099278C2semidirect
5. C2×#19099265C2semidirect
6. C2×#19099255C2semidirect
7. C2×#19099239C2semidirect
8. C2×#19099232C2semidirect
9. C2×#19099217C2semidirect
10. C2×#19099206C2semidirect
11. C2×#19099200C2semidirect
12. C2×D4×C22⋊D79C2semidirect
13. C2×#19099182C2semidirect
14. C2×#19099166C2semidirect
15. C2×#19099164C2semidirect
16. C2×#19099149C2semidirect
17. C2×#19099141C2semidirect
18. C2×#19099129C2semidirect
19. C2×#19099128C2semidirect
20. C2×#19099125C2semidirect
21. C2×#19099076C2semidirect
22. C2×#19099072C2semidirect
23. C22×#14579132C2semidirect
24. C2×#546×C79C2semidirect
25. C22×#11929625C22semidirect
26. C22×#11929624C22semidirect
27. C22×#11929623C22semidirect
29. C23×C22⋊D79C22semidirect
30. C22×D4×D79C22semidirect
31. C23×C4×D79C22semidirect
32. #19099310C22semidirect
33. #19099301C22semidirect
34. #19099278C22semidirect
35. #19099265C22semidirect
36. #19099255C22semidirect
37. #19099239C22semidirect
38. #19099232C22semidirect
39. #19099217C22semidirect
40. #19099206C22semidirect
41. #19099200C22semidirect
42. D4×C22⋊D79C22semidirect
43. #19099182C22semidirect
44. #19099166C22semidirect
45. #19099164C22semidirect
46. #19099149C22semidirect
47. #19099141C22semidirect
48. #19099129C22semidirect
49. #19099128C22semidirect
50. #19099125C22semidirect
51. C2×#14579161C22semidirect
52. C2×#14579157C22semidirect
53. C2×#14579157C22semidirect
54. C2×#14579157C22semidirect
55. C2×#14579156C22semidirect
56. C2×#14579154C22semidirect
57. C2×#14579154C22semidirect
58. C2×#14579152C22semidirect
59. C2×#14579152C22semidirect
60. C2×#14579147C22semidirect
61. C2×#14579147C22semidirect
62. C2×#14579147C22semidirect
63. C2×#14579147C22semidirect
64. #19099076C22semidirect
65. #19099072C22semidirect
66. C2×#14579146C22semidirect
67. C2×#14579146C22semidirect
69. C2×#14579145C22semidirect
70. C2×#14579145C22semidirect
71. C2×#14579145C22semidirect
72. C2×#14579145C22semidirect
73. C2×#14579144C22semidirect
74. C2×#14579143C22semidirect
75. C2×#14579143C22semidirect
76. C2×#14579143C22semidirect
77. C2×#14579141C22semidirect
78. C2×#14579140C22semidirect
79. C2×#14579139C22semidirect
80. C2×#14579138C22semidirect
81. C2×#14579138C22semidirect
82. C2×#14579137C22semidirect
83. C2×#14579137C22semidirect
84. C2×#14579136C22semidirect
86. C2×#14579135C22semidirect
87. C2×#14579135C22semidirect
88. C2×#14579135C22semidirect
89. C2×#14579135C22semidirect
90. C2×#14579135C22semidirect
91. C2×#14579134C22semidirect
92. C2×#14579134C22semidirect
93. C2×#14579134C22semidirect
95. C2×#14579133C22semidirect
96. C2×#14579133C22semidirect
97. C2×#14579133C22semidirect
98. C2×#14579133C22semidirect
101. C2×#14579132C22semidirect
102. C2×#14579132C22semidirect
103. C2×#14579132C22semidirect
104. C2×#14579132C22semidirect
105. C2×#14579132C22semidirect
106. C2×#14579132C22semidirect
107. C2×#14579132C22semidirect
109. C2×#14579131C22semidirect
110. C2×#14579131C22semidirect
111. C2×#14579131C22semidirect
113. C2×#14579129C22semidirect
114. C2×#14579129C22semidirect
115. C2×#14579129C22semidirect
116. C2×Q8×Dic79C22semidirect
117. C2×C4×D316C22semidirect
118. C2×C4×D316C22semidirect
119. C2×D4×Dic79C22semidirect
120. C2×D4×Dic79C22semidirect
121. C2×#14579123C22semidirect
123. C2×C4×C22⋊D79C22semidirect
124. C2×C4×C22⋊D79C22semidirect
125. C2×(C22⋊D79)⋊C4C22semidirect
126. C2×#14579120C22semidirect
127. C2×#14579119C22semidirect
128. C2×#14579119C22semidirect
129. C2×#14579118C22semidirect
130. C2×#14579117C22semidirect
131. C22×C4⋊Dic79C22semidirect
132. C22×C4⋊Dic79C22semidirect
133. C22×C22⋊Dic79C22semidirect
134. C2×C22⋊C4×D79C22semidirect
135. C22×#41×C79C22semidirect
137. #546×C79C22semidirect
138. C2×#124×C79C22semidirect
139. C2×#123×C79C22semidirect
140. C2×C22⋊Q8×C79C22semidirect
141. C2×#121×C79C22semidirect
142. C2×#121×C79C22semidirect
143. C2×#120×C79C22semidirect
144. C2×C4×D4×C79C22semidirect
145. C2×C4×D4×C79C22semidirect
146. C22×C22⋊C4×C79C22semidirect
150. C2×#11929625C23semidirect
152. C2×#11929624C23semidirect
154. C2×#11929623C23semidirect
179. C22×C22⋊D79C23semidirect
181. C2×D4×D79C23semidirect
194. C22×C4×D79C23semidirect
195. #14579161C23semidirect
196. #14579157C23semidirect
197. #14579157C23semidirect
198. #14579157C23semidirect
199. #14579156C23semidirect
200. #14579154C23semidirect
201. #14579154C23semidirect
202. #14579152C23semidirect
203. #14579152C23semidirect
204. #14579147C23semidirect
205. #14579147C23semidirect
206. #14579147C23semidirect
207. #14579147C23semidirect
208. #14579146C23semidirect
209. #14579146C23semidirect
211. #14579145C23semidirect
212. #14579145C23semidirect
213. #14579145C23semidirect
214. #14579145C23semidirect
215. #14579144C23semidirect
216. #14579143C23semidirect
217. #14579143C23semidirect
218. #14579143C23semidirect
219. #14579141C23semidirect
220. #14579140C23semidirect
221. #14579139C23semidirect
222. #14579138C23semidirect
223. #14579138C23semidirect
224. #14579137C23semidirect
225. #14579137C23semidirect
226. #14579136C23semidirect
228. #14579135C23semidirect
229. #14579135C23semidirect
230. #14579135C23semidirect
231. #14579135C23semidirect
232. #14579135C23semidirect
233. #14579134C23semidirect
234. #14579134C23semidirect
235. #14579134C23semidirect
237. #14579133C23semidirect
238. #14579133C23semidirect
239. #14579133C23semidirect
240. #14579133C23semidirect
243. #14579132C23semidirect
244. #14579132C23semidirect
245. #14579132C23semidirect
246. #14579132C23semidirect
247. #14579132C23semidirect
248. #14579132C23semidirect
250. #14579131C23semidirect
251. #14579131C23semidirect
252. #14579131C23semidirect
254. #14579129C23semidirect
255. #14579129C23semidirect
256. #14579129C23semidirect
257. Q8×Dic79C23semidirect
258. C4×D316C23semidirect
259. C4×D316C23semidirect
260. D4×Dic79C23semidirect
261. D4×Dic79C23semidirect
262. #14579123C23semidirect
264. C4×C22⋊D79C23semidirect
265. C4×C22⋊D79C23semidirect
266. (C22⋊D79)⋊C4C23semidirect
267. #14579120C23semidirect
268. #14579119C23semidirect
269. #14579119C23semidirect
270. #14579118C23semidirect
271. #14579117C23semidirect
281. C2×C4⋊Dic79C23semidirect
282. C2×C4⋊Dic79C23semidirect
298. C2×C22⋊Dic79C23semidirect
313. C22⋊C4×D79C23semidirect
320. C2×#41×C79C23semidirect
334. #124×C79C23semidirect
335. #123×C79C23semidirect
336. C22⋊Q8×C79C23semidirect
337. #121×C79C23semidirect
338. #121×C79C23semidirect
339. #120×C79C23semidirect
340. C4×D4×C79C23semidirect
341. C4×D4×C79C23semidirect
352. C2×C22⋊C4×C79C23semidirect
714. C2×C79#3542semidirect
733. C2×#546D79semidirect
746. C79C2×#3542semidirect
750. C22×#41C2×D79semidirect
766. #546C2×D79semidirect
789. C2×#124C2×D79semidirect
803. C2×#123C2×D79semidirect
811. C2×C22⋊Q8C2×D79semidirect
836. C2×#121C2×D79semidirect
837. C2×#121C2×D79semidirect
846. C2×#120C2×D79semidirect
857. C2×C4×D4C2×D79semidirect
858. C2×C4×D4C2×D79semidirect
868. C22×C22⋊C4C2×D79semidirect
879. C2×#41C22×D79semidirect
946. #124C22×D79semidirect
958. #123C22×D79semidirect
966. C22⋊Q8C22×D79semidirect
990. #121C22×D79semidirect
991. #121C22×D79semidirect
1000. #120C22×D79semidirect
1011. C4×D4C22×D79semidirect
1012. C4×D4C22×D79semidirect
1070. C2×C22⋊C4C22×D79semidirect
1439. C2#23777702direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237777022
C2×#190993102
C2×#190993012
C2×#190992782
C2×#190992652
C2×#190992552
C2×#190992392
C2×#190992322
C2×#190992172
C2×#190992062
C2×#190992002
C2×D4×C22⋊D792
C2×#190991822
C2×#190991662
C2×#190991642
C2×#190991492
C2×#190991412
C2×#190991292
C2×#190991282
C2×#190991252
C2×#190990762
C2×#190990722
C22×#145791322
C2×#546×C792
C2×#354279